Final answer:
The correct answer is D. Angular momentum about CM, as the application of a couple introduces a pure rotational effect that conserves angular momentum while potentially altering the rotational kinetic energy.
Step-by-step explanation:
When a couple is applied to a rigid body, it will create a pure rotational effect without affecting the center of mass's translational motion. The various forms of kinetic energy in this scenario include translational kinetic energy, which is associated with the body's movement through space, and rotational kinetic energy, which is associated with the body's spinning about its center of mass (CM).
The application of a couple does not exert any net force to change the translational motion, hence the translational kinetic energy (Translation K.E.) of the body remains unchanged. Similarly, the angular momentum about the center of mass is conserved because the couple does not exert any external net force, just a torque that may change the body's rotational speed but not its angular momentum. Therefore, considering conservation of angular momentum, the correct answer is D. Angular momentum about CM remains unchanged.
On the other hand, the rotational kinetic energy (Rotational K.E.) can change since a couple can do work on the system and change the rotational speed. Total kinetic energy (Total K.E.) might also change as it is the sum of translational and rotational kinetic energy. If a couple alters the rotational part, the total could change.